Bevel gear bevel angle measuring device and method

Abstract

The application discloses a bevel gear bevel angle measuring device and method, and relates to the technical field of gear measurement. The device comprises the following steps: obtaining displacement parameters and mechanical parameters of a target bevel gear under different inclination conditions, establishing a mapping relationship between the displacement parameters, the mechanical parameters and the bevel angle; establishing a coordinate system based on the installation position of the target bevel gear, and uniformly mapping the displacement and the mechanical parameters collected in the measuring process into the coordinate system; and setting a tactile probe in contact with the tooth surface under a preset load condition. The application establishes a coordinate system consistent with the gear installation reference, uniformly maps the displacement and the mechanical parameters to a standard reference frame, and expands the three-dimensional coordinates in combination with the gear rotation angle, so that complete description of the spatial position of the tooth surface is realized, and the distribution characteristics of the bevel angle in the tooth height direction and the circumferential direction can be intuitively presented, thereby providing visual judgment basis for the uniformity of the tooth surface angle and the design compliance.

Description

Technical Field

[0001] This invention relates to the field of gear measurement technology, specifically to a device and method for measuring the angle of inclined plane gears. Background Technology

[0002] As an important transmission component, helical gears are widely used in high-precision fields such as automobile manufacturing. The helical angle (including the slope angle of the planar helical surface and the tooth inclination angle of the tortuous helical surface) directly affects the meshing accuracy, transmission efficiency and service life of the gear. Therefore, it is necessary to design a device and method for measuring the helical angle of helical gears.

[0003] A search revealed that Chinese utility model patent application CN211651577U proposes a "sloping contact surface gauge for a centrifuge large gear assembly." The gauge features a sloping surface adapted to the outer edge of the large gear teeth, and gripping portions on both sides perpendicular to the insertion direction. The high-speed and low-speed shaft sloping contact surface gauge includes a gauge body with a sloping surface adapted to the tooth slopes of the high-speed and low-speed shafts, and gripping portions on both sides perpendicular to the insertion direction. This design allows for the detection of very small angles on the sloping surfaces of the large gear teeth in a centrifuge's high-precision large gear assembly, as well as the sloping surfaces of adjacent teeth on the high-speed and low-speed shafts. It also allows for the detection of a single shaft meshing with the gear after testing, avoiding the problem of excessive noise caused by even slightly large clearances at high speeds (hundreds of thousands of revolutions per minute). This solves the previous problem of large clearances caused by ineffective detection due to excessively small sloping surface angles.

[0004] Furthermore, Chinese invention patent application with publication number "CN112378345A" proposes a "gear angle offset measuring device and method based on laser displacement sensor". This method involves a workpiece rotary table and a two-axis translation mechanism on a worktable. The two-axis translation mechanism includes an X-axis guide rail fixed to the upper side of the worktable, a central positioning spindle vertically mounted on the workpiece rotary table, a Y-axis guide rail slidably connected to the X-axis guide rail, a lifting frame slidably connected to the Y-axis guide rail, and a laser displacement sensor connected to the lifting frame. The center plane of the X-axis guide rail passes through the center of the workpiece rotary table. The laser displacement sensor base is an adjustable-angle indexing plate, allowing adjustment of the indexing plate to change the position of the laser beam relative to the gear center for offset measurement, thereby achieving the measurement of complex gears.

[0005] However, the aforementioned devices and similar existing devices and methods are prone to failure in actual operation and measurement when optical and laser detection methods are present on the gear surface with oil film, emulsion or metallic luster reflection, and have insufficient anti-interference ability, making them difficult to apply to complex workshop environments and on-site maintenance scenarios. Summary of the Invention

[0006] The purpose of this invention is to provide a device and method for measuring the inclined plane angle of inclined gears, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: Firstly, a method for measuring the inclined plane angle of a helical gear is proposed, including: Obtain the displacement and mechanical parameters of the target inclined gear under different inclination angles, and establish the mapping relationship between the displacement and mechanical parameters and the inclination angle; A coordinate system is established based on the installation position of the target inclined gear, and the displacement and mechanical parameters collected during the measurement process are uniformly mapped to the coordinate system; Under preset load conditions, the tactile probe is set to contact the tooth surface, and small displacement sampling is performed along the local area of ​​the tactile probe to obtain the displacement sequence of the trajectory point and the corresponding mechanical response sequence. The collected displacement sequence and mechanical response sequence are fitted to either a plane or a curved surface to obtain the normal vector of the local inclined surface of the target inclined gear tooth surface; The angle between the fitted normal vector and any one of the gear axis or reference plane is calculated to obtain the numerical output of the tooth surface helical angle.

[0008] As a further preferred embodiment of this technical solution, the method for constructing the mapping relationship includes: Under the conditions of standard gears or calibration samples with known inclined plane angles, displacement parameters and mechanical parameters at different inclined plane angles are collected, and a basic dataset containing multiple inclined plane angle sample points is formed. The collected data is preprocessed to eliminate random noise introduced by workshop vibration and electromagnetic interference. The preprocessed displacement parameters and mechanical parameters are combined to construct a multidimensional feature vector, and the known inclined plane angle values ​​of different parts are labeled to form a “feature vector - inclined plane angle” correspondence. Based on the comparison relationship, a slope angle mapping function reflecting the combined effect of displacement parameters and mechanical parameters is established; The inclined plane angle mapping function was verified and optimized using a reference inclined plane gear with a known standard angle.

[0009] As a further preferred embodiment of this technical solution, the horizontal coordinate of the coordinate system represents the radial direction of the gear, denoted as the r-axis. The origin of the coordinate system is set as the intersection of the gear reference end face and the gear reference axis. The vertical coordinate represents the axial direction of the gear, denoted as the z-axis. When the upper value of the z-axis is zero, the z-axis coincides with the gear reference end face. The upper value of the z-axis is positive along the gear width direction.

[0010] As a further preferred embodiment of this technical solution, for the displacement parameters, the radial distance from the reference end face to the tooth surface contact point directly corresponds to the r coordinate value of the contact point in the coordinate system, and the axial offset of the probe relative to the reference axis when it contacts the tooth surface corresponds to the z coordinate value of the contact point in the coordinate system. That is, each tooth surface contact point uniquely corresponds to a coordinate point (r, z) in the coordinate system.

[0011] As a further preferred embodiment of this technical solution, for mechanical parameters, the direction of the normal force is along the normal direction of the tooth surface, which is used to decompose it into a component force in the r-axis direction and a component force in the z-axis direction, and the direction of the mechanical parameters is associated with the position of the displacement parameters through the coordinate system.

[0012] As a further preferred embodiment of this technical solution, the preset load condition refers to collecting displacement and mechanical parameters along the tooth length direction or tooth height direction within the measurement range of the tooth surface to be measured of the target inclined gear. Micro-displacement sampling refers to obtaining the displacement sequence and corresponding mechanical response sequence along the selected measurement line of the target inclined gear in a continuous or segmented manner.

[0013] As a further preferred embodiment of this technical solution, the method for obtaining the normal vector includes: The three-dimensional coordinates of the collected trajectory points are associated with the corresponding displacement parameters and mechanical parameters to form a local point cloud of the tooth surface; Based on the gear type of the helical gear, the fitting method is determined and the normal vector is obtained; For planar helical gears, the helical surface of a planar helical gear can be regarded as a plane unfolded along the tooth direction. Its geometric feature is that there is a fixed inclination angle only in the radial direction and the axial direction. For gears with twisted inclined planes, multiple sampling points are performed in the tooth direction using a probe to record the displacement changes at different tooth positions under the same radial-axial slope. Then, by combining the geometric relationship between the tooth direction and the radial and axial directions, the tilt angle of the inclined plane in the tooth direction can be deduced.

[0014] As a further preferred embodiment of this technical solution, the inclination angle of the planar inclined gear is the slope angle. When the probe gradually contacts the inclined plane from the reference end face of the gear, if the inclined plane is steeper, the probe will produce a larger axial displacement under the same radial displacement, thereby increasing the value of the slope angle. Conversely, if the inclined plane is gentle, the displacement of the tactile probe along the axial direction is smaller, and the slope angle will also decrease accordingly. For gears with twisted inclined planes, the inclination angle is the tooth inclination angle. By sampling multiple points along the tooth direction with a probe, the displacement changes at different tooth positions under the same radial-axial slope are recorded. Combined with the geometric relationship between the tooth direction and the radial and axial directions, the inclination angle of the inclined plane in the tooth direction can be deduced. When the tooth inclination angle is zero, it means that the inclined plane is only tilted in the radial-axial direction, with no tooth offset. The normal vector is the same as that of the planar inclined plane gear. When the tooth inclination angle increases, it means that the inclined plane has more significant twisting or helical movement in the tooth direction, and the normal vector gradually deviates from the radial-axial plane.

[0015] Secondly, to improve the above technical solution, a device for measuring the inclined plane angle of inclined gears was also proposed, which uses the above-mentioned method for measuring the inclined plane angle of inclined gears.

[0016] Compared with the prior art, the beneficial effects of the present invention are: The inclined plane angle measuring device and method for inclined gears can directly measure the inclined plane angle inside the machine tool without transferring the workpiece to a special testing equipment, thereby significantly shortening the process changeover time and ensuring processing cycle time and production efficiency; In addition, by simultaneously acquiring multi-dimensional parameters such as radial displacement, axial displacement, normal force, radial component force, peak force, and force rise time of the tactile probe, and establishing a mapping relationship with the inclined plane angle, the initial measurement error can be effectively eliminated, ensuring the accuracy and repeatability of the measurement results. It should also be noted that by establishing a coordinate system consistent with the gear mounting datum, displacement and mechanical parameters are uniformly mapped to the standard reference frame, and combined with the gear rotation angle to expand into three-dimensional coordinates, a complete description of the spatial position of the tooth surface is realized. This allows for a direct presentation of the distribution characteristics of the inclined plane angle in the tooth height direction and the circumferential direction, providing a visual basis for judging the uniformity of the tooth surface angle and the design compliance. It should also be noted that by adopting trajectory-based micro-displacement sampling, it is possible to fully cover the tooth height direction of spur gears and the helical direction of helical gears, obtain multi-point sequence data, and truly reflect the angular deviations at both ends of the tooth tip and tooth root, and tooth width. Combined with the real-time adjustment of the probe contact force by the servo system, it ensures the stability of the contact state during the sampling process, avoids measurement deviations caused by force fluctuations, and thus ensures the consistency and stability of the measurement. Attached Figure Description

[0017] Figure 1 This is a flowchart of the steps of the method disclosed in this invention; Figure 2 This is an auxiliary illustration of step S100 of the present invention; Figure 3 This is an auxiliary illustration of step S104 of the present invention; Figure 4 This is a diagram showing the angle distribution of the beveled surface of the tooth surface in this invention; Figure 5 This is a diagram illustrating the single-trajectory mechanics and displacement sequence of the present invention. Figure 6 This is a schematic diagram of the angle of the three-dimensional tooth surface slope of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Before understanding the technical solution proposed in this invention, it is important to understand that in gear manufacturing workshops, tooth surfaces are often affected by oil stains, metallic luster, or vibration interference, which can easily affect traditional optical methods. However, tactile measurement can work stably in this environment and can be used for semi-finishing and finished product inspection to quickly detect errors in inclined surface machining. For example, in machine tool inspection, angle measurement can be performed directly inside the machine tool, thereby shortening process changeover time and improving processing efficiency. In addition, it should be noted that in gearbox maintenance and lubrication environments, where oil films and emulsions often cause optical failure, the tactile solution can still achieve effective detection and meet on-site maintenance needs.

[0020] like Figure 1 As shown, the present invention provides a technical solution: a method for measuring the inclined plane angle of an inclined gear, comprising: steps S100-S500.

[0021] Step S100: Obtain the displacement and mechanical parameters of the target inclined gear under different inclination angles, and establish the mapping relationship between the displacement and mechanical parameters and the inclined angle.

[0022] It should be noted that step S100 in this technical solution is mainly used to establish a mapping relationship. The mapping relationship aims to eliminate initial errors and ensure the accuracy and repeatability of subsequent measurements. Furthermore, the displacement parameters defined in this solution are specifically: the feed displacement Δr of the tactile probe along the direction perpendicular to the gear axis (i.e., radial), and the offset displacement Δz of the probe along the direction parallel to the gear axis (i.e., axial). Here, Δr represents the radial distance the probe moves from the gear reference end face (e.g., the gear positioning end face) to the tooth surface contact point, directly reflecting the radial position change of the tooth surface. Δz represents the axial offset of the probe relative to the gear reference axis (e.g., the gear rotation axis) when it contacts the tooth surface, corresponding to the probe position offset caused by the axial inclination of the tooth surface slope. Both Δr and Δz are collected in real time by the high-precision displacement sensor integrated into the existing probe. These components together constitute the displacement information characterizing the position of the inclined plane on the gear tooth surface, providing basic data for establishing its mapping relationship with the inclined plane angle. In this technical solution, the probe refers to a tactile integrated probe mounted on the machine tool spindle. It integrates dual-axis high-precision displacement sensors (such as grating sensors or inductive sensors with a resolution of up to 0.1μm in the prior art) in the radial (i.e., perpendicular to the gear axis direction) and axial (i.e., parallel to the gear axis direction) directions. These sensors are used to collect the Δr and Δz displacement data of the probe contact with the gear tooth surface in real time and synchronously. It should be noted that the contact end of the probe adopts a spherical structure and is made of tungsten carbide alloy or zirconium oxide ceramic with excellent wear resistance to cope with the harsh environment that may exist on the gear tooth surface in the gear manufacturing workshop, such as metal burrs and oil stains, and to avoid contact point position deviation caused by contact wear.

[0023] Accordingly, the mechanical parameters defined in this scheme specifically include: the normal force Fn perpendicular to the tooth surface that the tactile probe experiences when it contacts the tooth surface, and the component force Fr along the radial feed direction of the probe. Fn directly reflects the contact state between the tooth surface and the probe, and its value is directly proportional to the slope angle. When the slope angle increases, the probe needs to overcome a larger normal resistance component to maintain stable contact with the tooth surface, resulting in a significant increase in Fn. Fr is the reverse resistance experienced by the probe during radial feed. The direction of Fr is opposite to the feed direction, and its value fluctuates linearly with the slope angle. Since the slope inclination changes the direction of the force exerted by the tooth surface on the probe, the deviation of the slope angle can be indirectly inferred through the trend of Fr's change.

[0024] In addition, the mechanical parameters also include the dynamic characteristic values ​​of the force signal, namely the peak force Fmax and the force rise time tr. Fmax is the maximum force at the moment the probe contacts the tooth surface. The value of Fmax is closely related to the steepness of the tooth surface slope and the surface roughness. The larger the slope angle, the larger Fmax. tr is defined as the time history from the initial contact of the probe with the tooth surface to the reaching of the peak force, reflecting the tilt rate of the tooth surface slope. The larger the slope angle, the shorter tr. It should be added that the above mechanical parameters are collected in real time by a high-precision piezoelectric force sensor built into the probe (sampling frequency ≥ 1 kHz), and together with the displacement parameters Δr and Δz, they form a multi-dimensional feature vector.

[0025] As a preferred implementation scheme, refer to Figure 2 It can be seen that the method for constructing the mapping relationship includes: steps S101-S105.

[0026] Step S101: Under the condition of a standard gear or a calibration sample with a known inclined plane angle, use a tactile integrated probe installed on the machine tool spindle to collect displacement parameters Δr, Δz and mechanical parameters Fn, Fr, Fmax, tr under different inclined plane angles to form a basic dataset containing multiple inclined plane angle sample points.

[0027] It should be noted that in step S101, the basic dataset serves as a training sample library for establishing the mapping relationship, providing a source of original data with real physical meaning, and laying the experimental foundation for the subsequent establishment of the mapping function.

[0028] Step S102: Preprocess the collected data, including performing noise filtering and signal smoothing on displacement and mechanical signals to eliminate random noise introduced by workshop vibration and electromagnetic interference.

[0029] It should be noted that the purpose of step S102 is to normalize and unify the displacement and mechanical parameters to avoid fitting deviations caused by differences in dimensions, and to remove outlier data with obvious anomalies, so as to ensure the stability and accuracy of the mapping relationship modeling, improve the purity and consistency of the input data, and ensure that the model construction is not affected by noise and outlier data.

[0030] Step S103: Combine the preprocessed displacement parameters Δr and Δz with the mechanical parameters Fn, Fr, Fmax, and tr to construct a multidimensional feature vector, and label it according to the known inclined plane angle values ​​of different parts to form a “feature vector-inclined plane angle” correspondence, thereby providing supervised training data for establishing the mapping function.

[0031] Step S104: Based on the comparison relationship, establish a slope angle mapping function that reflects the combined effect of displacement parameters and mechanical parameters.

[0032] In a preferred embodiment, the inclined plane angle mapping function is implemented using linear regression modeling. Specifically, firstly, the displacement parameters and mechanical parameters are standardized to obtain standardized feature vectors (e.g., standardized Δr = Δr / Δrmax, standardized Fn = Fn / Fmax, where Δr_max and Fmax are the maximum sample values ​​of the corresponding features), eliminating the influence of dimensional differences on the model. Then, the standardized multidimensional feature vectors are set as the independent variable matrix X (dimension n×m, where n is the number of samples and m is the number of features, including 6 standardized features: Δr, Δz, Fn, Fr, Fmax, and tr). An intercept term is introduced to construct an augmented matrix Xaug = [1, X] (where 1 represents a column vector of all 1s). With the known inclined plane angle value as the dependent variable vector Y (dimension n×1), a linear regression model is constructed: Y = X_aug·β+ε, where β=[β0, β1, ..., β m ] ᵀ The regression coefficient vector (β0 is the intercept term, β1 to β...) m (where E(ε) is the regression coefficient of each standardized feature), and ε is the random error vector, satisfying E(ε) = 0 and Var(ε) = σ. 2 Assuming Gaussian assumptions about I (where I is the identity matrix), the regression coefficient β is estimated using the least squares method, which is based on minimizing the sum of squared residuals SSE = Σ(yi - ŷi). 2 It should be noted that (yi is the true slope angle of the i-th sample, ŷi=X_aug, i·β̂ is the model prediction value) the optimal estimate of β is calculated by the formula: β̂ = (X_augᵀX_aug) -1 X_augᵀY.

[0033] Step S105: Verify the inclined plane angle mapping function using a reference inclined plane gear with a known standard angle, compare the deviation between the measurement results and the theoretical angle, and correct and optimize the parameters of the inclined plane angle mapping function based on the residual analysis results.

[0034] It should be noted that the purpose of step S105 is to ensure that the model is not only effective under theoretical conditions, but also maintains high accuracy and stability in the actual complex environment of the workshop.

[0035] Specifically, participate Figure 3As can be seen, for the inclined plane angle mapping function disclosed in step S104, the specific content of the correction and optimization in step S105 is as follows: First, for the measurement data of the control inclined plane gear, calculate the residual of each sample (the difference between the actual inclined plane angle and the angle predicted by the mapping function), draw the residual histogram and the scatter plot of the residual and the predicted value, verify whether the residual conforms to the normal distribution through the Shapiro-Wilk test in the prior art (p value > 0.05 is acceptable), and use the Breusch-Pagan test in the prior art to judge whether the residual variance is homogeneous (p value > 0.05 is considered stable). If the residual shows obvious non-normal distribution or heteroscedasticity, it indicates that the linear model has failed to fully capture the complex relationship between the feature and the inclined plane angle, and the model structure needs to be further adjusted.

[0036] Secondly, model structure optimization should be performed based on residual characteristics. If the residuals exhibit a monotonically increasing or decreasing nonlinear trend with the predicted values, nonlinear terms or interaction terms of the features need to be introduced to expand the model's expressive power. For example, adding Δr... 2 Quadratic terms or cross terms such as Δz·Fn, Fr·Fmax, etc., are used to upgrade the original linear model to a quadratic polynomial regression model; if the variance inflation factor (VIF) test reveals severe multicollinearity (VIF > 5) among the features, Ridge regularized regression, a technique already in use, is used to constrain the newly added content.

[0037] Finally, the optimized mapping function is used to re-predict the control gear, and the corrected prediction deviation (such as maximum absolute deviation, mean absolute deviation, and standard deviation) is calculated and compared with the preset accuracy threshold (such as ±0.05° required by the workshop inspection). If the deviation meets the requirements, the mapping function is determined to be the final model; if the deviation does not meet the requirements, it is necessary to return to step S101 to supplement boundary samples or sample data with large deviations, or reconsider feature selection (such as adding new mechanical parameters) until the model accuracy meets the requirements of field application.

[0038] Step S200: Establish a coordinate system based on the installation position of the target inclined gear, and map the displacement and mechanical parameters collected during the measurement process into the coordinate system.

[0039] It should be noted that step S200 in the technical solution proposed in this application is mainly used to realize the benchmarking of data, to ensure that data from different measurement points and under different measurement conditions are comparable. Specifically, it enables data from different measurement points to be used for direct comparison, ensuring data consistency and providing a basis for subsequent angle calculation.

[0040] It should be added that in step S200, the horizontal coordinate of the coordinate system represents the radial direction of the gear (i.e., the direction perpendicular to the gear reference axis), denoted as the r-axis. Its origin is set at the intersection of the gear reference end face (i.e., the positioning end face that fits against the machine tool table during gear installation) and the gear reference axis (i.e., the gear rotation axis, whose coaxiality is ensured by the machine tool spindle positioning). The vertical coordinate represents the axial direction of the gear (i.e., the direction parallel to the gear reference axis), denoted as the z-axis. It should be noted that the z=0 plane coincides with the gear reference end face, and the z value is along the gear width direction (away from the base). The direction of the reference end face is positive. In addition, it should be noted that the coordinate system is established based on the positioning reference of the gear installation to ensure consistency with the machine tool machining coordinate system. Specifically, the positioning accuracy of the machine tool spindle (such as radial runout ≤0.002mm) ensures that the gear reference axis is coaxial with the machine tool spindle axis, and the flatness of the worktable (≤0.001mm / 100mm) ensures that the gear reference end face is in contact with the worktable surface. Thus, the r-axis of the coordinate system is completely consistent with the radial feed direction of the probe, and the z-axis is completely consistent with the axial offset direction of the probe.

[0041] For displacement parameters, the radial distance Δr from the probe's radial feed from the reference end face (z=0) to the tooth surface contact point directly corresponds to the r coordinate value (r=Δr) of that contact point in the coordinate system. The axial offset Δz of the probe relative to the reference axis when it contacts the tooth surface corresponds to the z coordinate value (z=Δz) of that contact point in the coordinate system. That is, each tooth surface contact point uniquely corresponds to a coordinate point (r,z) in the coordinate system. For the mechanical parameters, the direction of the normal force Fn is along the normal direction of the tooth surface. It is used to decompose the force Fr in the r-axis direction (that is, the force in the radial feed direction of the probe defined in step S100, which is negative when it is opposite to the positive direction of the r-axis) and the force Fz in the z-axis direction (Fz=Fn·sinθ, where θ is the angle between the inclined surface of the tooth surface and the reference end face, that is, the angle of the inclined surface to be measured). The direction of mechanical parameters such as Fn and Fr can be associated with the position of displacement parameters through the coordinate system, so as to ensure that the directional characteristics of the mechanical signal correspond one-to-one with the position of the tooth surface in the coordinate system.

[0042] Furthermore, in the actual process of establishing a coordinate system, the rotation angle of the helical gear must also be considered. The tooth surface of the helical gear is spirally distributed along the circumference. Therefore, when measuring the tooth surface at different circumferential positions, the rotation angle α of the gear must be recorded by the rotation angle encoder (resolution ≥ 1 arcsecond) of the machine tool spindle. The coordinates of each contact point are extended into a three-dimensional form (r, z, α), thereby completely describing the position of the tooth surface contact point in the three-dimensional space of the gear. This ensures that the measurement data of different circumferential positions of the same tooth surface are correlated through the rotation angle α, further guaranteeing the consistency and comparability of the data.

[0043] Step S300: Under preset load conditions, set the tactile probe to contact the tooth surface, and perform micro-displacement sampling along the local area of ​​the tactile probe to obtain the displacement sequence of the trajectory point and the corresponding mechanical response sequence.

[0044] It should be noted that the preset load condition in step S300 specifically refers to collecting displacement and mechanical parameters along the tooth length direction or tooth height direction within the measurement range of the tooth surface to be measured of the target inclined gear. Micro-displacement sampling refers to obtaining the displacement sequence and corresponding mechanical response sequence along the selected measurement line of the target inclined gear in a continuous or segmented manner.

[0045] As a preferred implementation scheme, such as Figures 4 to 6 As shown, the tooth surface of a helical gear has a straight or helical inclined structure. Since the measurement of a single contact point is difficult to fully characterize the spatial distribution characteristics of the helical angle of the tooth surface, especially the angular deviation between the tooth tip and the tooth root region and the small fluctuations in the circumferential direction, in order to obtain complete spatial distribution information of the helical angle of the tooth surface, this scheme adopts a measurement method of laying out continuous sampling trajectories along the characteristic direction of the tooth surface. The specific implementation is as follows: (a) Trajectory layout and sampling point setting For spur gears with helical surfaces, the measurement trajectory is laid out along the tooth height direction, covering the area from the root circle to the tip circle. Each trajectory has 6 to 8 evenly distributed sampling points, with a radial spacing of ≤0.4 mm between adjacent points. The trajectory is laid out at four typical positions along the gear circumference (e.g., α = 30°, 120°, 210°, 300°) to ensure comprehensive acquisition of local features of the tooth surface.

[0046] It should be noted that, among them Figure 4 The diagram shows the distribution of the bevel angles on the tooth surface. The horizontal axis represents the gear's circumferential angle α, the vertical axis represents the tooth height r, and the color mapping corresponds to the θ value. Figure 4 The angle value at the tooth tip is slightly lower than that at the tooth root, and there are slight periodic fluctuations along the circumferential direction. The circular markers in the figure represent the sampling trajectory points of the probe, and the × markers indicate the location of local defects. Figure 4 Characterizing the overall spatial distribution trend of the bevel angle of the tooth surface provides a basis for trajectory layout and defect detection. It should be noted that... Figure 4 This indicates that the change in helix angle is difficult to visualize and needs to be combined with... Figure 6 Three-dimensional schematic diagrams are used for spiral characteristic analysis.

[0047] For helical gears, the measurement trajectory is laid out along the helical line of the tooth surface, in the same direction as the gear's rotation. The sampling point spacing is dynamically adjusted according to the helix angle: when the helix angle is ≥15°, the spacing is ≤0.3 mm; when the helix angle is <15°, the spacing is ≤0.5 mm. It should be noted that the initial circumferential angle is distributed across the four quadrants of the gear to ensure the helical trajectory covers the entire tooth surface. Additionally, it should be added that... Figure 6The diagram shows a 3D tooth surface bevel angle. The θ value is mapped to the Z-axis height: X = rcosα, Y = rsinα. Figure 6 It intuitively presents the tooth surface inclination and helical characteristics, providing a basis for trajectory spatial layout, while clearly showing the spatial location of abnormal points on the tooth surface.

[0048] (ii) Force-controlled feed of tactile probe The tactile probe feeds at a constant low speed (0.05~0.1 mm / s) along a preset trajectory, precisely controlled by the machine tool servo system. Upon reaching each sampling point, the probe's built-in force sensor provides real-time feedback of the normal force Fn, and the machine tool spindle dynamically adjusts the Z-axis feed to stabilize Fn within a preset threshold range. When the module is ≥3 mm, Fn = 8 to 10 N; When the module is less than 3 mm, Fn = 5 to 7 N.

[0049] It should be noted that, in combination Figure 5 As shown in the single-trajectory mechanics and displacement sequence diagram, the upper subplot displays the variation of Fn with tooth height r and local anomalies, while the lower subplot displays the radial displacement Δr. This diagram can be used to identify potential defects on the tooth surface (such as burrs or pits) and to verify the stability of force-controlled feed.

[0050] (III) Data Acquisition and Spatial Sequence Generation The following parameters are recorded for each sampling point: Spatial coordinates: r = Δr (radial displacement), z = Δz (axial displacement), α (real-time encoder output); mechanical parameters: Fn, Fr, Fmax, tr.

[0051] This generates a sequence of "spatial coordinates - feature parameters" data. After the sequence data is input into the mapping function (step S100), a spatial distribution map of the tooth surface inclined angle can be generated. Figure 4 (where the x-axis is α, the y-axis is r, and the color mapping represents the θ value). Based on this, we can analyze: The difference in angle between the tooth tip and the tooth root (pass criterion: θ_tip - θ_root ≤ 0.03°); Minor circumferential fluctuations (criterion: ≤0.02°); Location and severity of local defects.

[0052] Sequence data supports multi-dimensional analysis: by combining mechanical parameters, displacement changes, and friction time (tr), the contact quality and friction characteristics of the tooth surface can be evaluated, providing a basis for process optimization or tooth surface modification.

[0053] (iv) Anomaly detection and defect verification Abnormal points on the tooth surface can be identified through sequence data analysis: A sudden increase in Fmax of ≥20% suggests a localized abnormality on the tooth surface. A sudden decrease in Δr can further verify the location of the depression or spur.

[0054] It should be added that this implementation scheme, through continuous trajectory sampling, closed-loop force-controlled feed, and sequence data analysis, can comprehensively and accurately obtain the spatial distribution information of the bevel angle of the tooth surface, and simultaneously realize defect detection and tooth surface uniformity evaluation. Figures 4 to 6 The study presents trajectory layout strategies, measurement data, and three-dimensional inclined plane structures, providing intuitive and quantifiable evidence for the inspection and design verification of inclined gears. It can be regarded as the preferred solution for tooth surface measurement and defect detection.

[0055] Step S400: Fit the acquired displacement sequence and mechanical response sequence to any one of the plane or curved surface to obtain the normal vector of the local inclined surface of the target inclined gear tooth surface.

[0056] It should be clear that step S400 processes the displacement sequence and mechanical parameters collected by the tactile probe along the tooth surface trajectory in step S300 to obtain the normal vector of the local inclined plane of the tooth surface, thereby providing basic data for the calculation of the inclined plane angle. The specific implementation steps are as follows: Step S401: Associate the three-dimensional coordinates (r, z, α) of the collected trajectory points with the corresponding displacement parameters Δr, Δz and mechanical parameters Fn, Fr, Fmax, tr to form local point cloud data of the tooth surface.

[0057] It should be noted that in step S401, each trajectory point has a unique position coordinate and a corresponding feature parameter in the coordinate system, realizing the correspondence between "spatial coordinates and feature parameters".

[0058] Step S402: Based on the gear type of the helical gear, determine the fitting method and obtain the normal vector.

[0059] As a supplementary explanation to step S402, for a planar helical gear, the helical surface of the planar helical gear can be regarded as a plane unfolded along the tooth direction. Its geometric feature is that there is a fixed inclination angle only between the radial and axial directions. To describe the inclination characteristics of the planar helical gear, a slope angle ψ is defined. The value of the slope angle ψ represents the degree of inclination of the helical surface in the radial-axial section. The slope angle ψ can be calculated from the probe displacement parameters collected in step S100, i.e. .

[0060] It should be noted that Δr is the displacement of the tactile probe in the radial direction, and Δz is the displacement of the tactile probe in the axial direction. The meaning of the above formula is that when the probe gradually contacts the inclined plane from the gear reference end face, if the inclined plane is "steeper", the probe will produce a larger axial offset Δz under the same radial displacement Δr, thus increasing the value of the slope angle ψ. Conversely, if the inclined plane is "gentler", Δz is smaller, and ψ also decreases accordingly.

[0061] Furthermore, it should be noted that for gears with twisted inclined surfaces, in addition to the slope in the radial-axial direction, the inclined surface also has a certain tilt or helical feature in the tooth direction. To describe the characteristics of gears with twisted inclined surfaces, this invention introduces the tooth inclination angle λ, which is used to characterize the degree of deflection of the inclined surface in the tooth direction relative to the pure tangential direction. The tooth inclination angle λ is obtained by sampling at multiple points in the tooth direction with a probe, recording the displacement changes at different tooth positions under the same radial-axial slope, and then combining the geometric relationship between the tooth direction and the radial and axial directions to deduce the tilt angle λ of the inclined surface in the tooth direction.

[0062] It is worth noting that when λ=0, it means that the inclined plane is tilted only in the radial-axial direction, without tooth offset, and the normal vector is the same as in the first case. When λ increases, it means that the inclined plane has more significant twisting or spiraling in the tooth direction, the normal vector gradually deviates from the radial-axial plane, and increases its component in the tooth direction.

[0063] Therefore, the normal vector of the first type of inclined plane is determined only by the slope angle ψ, exhibiting a two-dimensional variation law; the normal vector of the second type of inclined plane is jointly determined by the slope angle ψ and the tooth inclination angle λ, exhibiting a three-dimensional variation law.

[0064] Step S500: Calculate the angle between the fitted normal vector and any one of the gear axis or reference plane to obtain the numerical output of the tooth surface inclined angle.

[0065] It should be added that, in step S500, the calculation of the tooth surface inclination angle is based on step S400, by fitting the local tooth surface of the sampling point to obtain the normal vector.

[0066] Specifically, ,in Approximately equal to the axial and radial displacement changes, taking sampling points 1 (r1, z1) and 3 (r3, z3) as examples, the radial displacement change between the two points is Δr = r3 - r1, and the axial displacement change is Δz = z3 - z1. The angle θ between the tooth surface and the reference end face (z = 0) is initially estimated as θ = arctan(Δz / Δr). To improve accuracy, three consecutive sampling points (such as sampling points 1, 2, and 3) are usually selected for plane fitting. In this technical solution, the plane equation is set as a·r + b·z + c = 0. Substituting the coordinates of the three points, we obtain the linear equation system: a·r1+b·z1+c=0 a·r² + b·z² + c = 0 a·r³ + b·z³ + c = 0 The coefficients a, b, and c are obtained by solving using the least squares method (after eliminating the influence of c, a / b = -Δz / Δr). The unit normal vector is (a,b) / √(a 2 +b 2 Since the normal vector of the reference end face is (0,1) (in the z-axis direction), and the angle θ of the tooth surface bevel is the angle between the normal vector and the z-axis, then cosθ=|b| / √(a 2 +b 2 ), that is, θ=arccos(|b| / √(a 2 +b 2 The calculation result is consistent with arctan(Δz / Δr), therefore the obtained tooth surface inclination angle is the inclination angle value of this local tooth surface.

[0067] As a supplement to the above technical solution, the present invention also proposes a device for measuring the inclined plane angle of a helical gear, which uses the above-mentioned method for measuring the inclined plane angle of a helical gear, and specifically includes: Machine tool positioning system: used to achieve the installation and positioning of the target inclined gear, including machine tool spindle and worktable. The machine tool spindle ensures rotational accuracy through high-precision bearing assembly with radial runout ≤0.002mm, and its axis is coaxial with the gear reference axis. The worktable adopts a granite platform with flatness ≤0.001mm / 100mm to support the gear reference end face, ensuring that the gear is consistent with the machine tool machining coordinate system during installation, and providing a mechanical reference for the coordinate system establishment in step S200.

[0068] Tactile probe assembly: Used to acquire the displacement sequence and mechanical response sequence of the tooth surface, including a high-precision tactile probe, a built-in force sensor and a displacement encoder. The probe of the tactile probe is made of tungsten carbide material with a tip radius ≤0.1mm to ensure point contact characteristics when in contact with the tooth surface. The force sensor has a resolution ≥0.01N and a range of 0-50N, and can provide real-time feedback of normal force Fn, radial component force Fr and maximum impact force Fmax. The displacement encoder has a linear measurement accuracy ≤0.001mm and a sampling frequency ≥1kHz, and is used to record the radial displacement Δr, axial displacement Δz and trajectory feed speed of the probe (error ≤±5%), providing data support for the micro-displacement sampling in step S300.

[0069] Rotary angle encoder: Installed at the end of the machine tool spindle, it adopts the photoelectric measurement principle, with a resolution of ≥1 arcsecond and a sampling frequency of ≥10kHz. It is used to record the rotation angle α of the gear in real time, and expands the coordinates of the tooth surface contact point into a three-dimensional form (r,z,α) to ensure that the measurement data of different circumferential positions of the same tooth surface are correlated, and further ensure the consistency of the data (as described in step S200).

[0070] Data acquisition and processing unit: includes a high-speed data acquisition card (sampling frequency ≥100kHz, resolution ≥16-bit) and an industrial computer. The data acquisition card is used to synchronously acquire the output signals of the tactile probe assembly and the rotary angle encoder to realize the sequential data storage of "spatial coordinates - feature parameters" (as described in step S300). The industrial computer has built-in existing programming algorithm software, which integrates plane fitting (least square method) and surface fitting (B-spline surface) algorithms to process the point cloud data in step S400 and solve for the local normal vector of the tooth surface. At the same time, the programming algorithm software also integrates a slope angle calculation module (such as the Arccos formula in step S500), a spatial distribution map generation module (with α as the abscissa, r as the ordinate, and color mapping θ value), and an anomaly detection module (setting the Fmax threshold to mean + 2 times standard deviation) to realize real-time processing and visualization output of measurement data.

[0071] The servo control system, used to drive the machine tool spindle rotation and the tactile probe feed, includes a servo motor (torque fluctuation ≤ ±1%), a ball screw (lead error ≤ 0.002 mm / 300 mm), and a linear guide (repeat positioning accuracy ≤ 0.001 mm). The position control accuracy of the servo system is ≤ 0.001 mm, and the speed control accuracy is ≤ ± 0.005 mm / s, ensuring that the probe feeds at a uniform speed (0.05-0.1 mm / s) along a preset trajectory (straight tooth height direction, helical tooth spiral direction) in step S300, and maintaining the normal force Fn within a preset threshold range (e.g., 8-10 N when the module is ≥ 3 mm), avoiding mechanical parameter deviations caused by contact force fluctuations.

[0072] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended embodiments and their equivalents.

Claims

1. A method for measuring the angle of the inclined plane of a helical gear, characterized in that, include: Obtain the displacement and mechanical parameters of the target inclined gear under different inclination angles, and establish the mapping relationship between the displacement and mechanical parameters and the inclination angle; A coordinate system is established based on the installation position of the target inclined gear, and the displacement and mechanical parameters collected during the measurement process are uniformly mapped to the coordinate system; Under preset load conditions, the tactile probe is set to contact the tooth surface, and small displacement sampling is performed along the local area of ​​the tactile probe to obtain the displacement sequence of the trajectory point and the corresponding mechanical response sequence. The collected displacement sequence and mechanical response sequence are fitted to either a plane or a curved surface to obtain the normal vector of the local inclined surface of the target inclined gear tooth surface; The angle between the fitted normal vector and any one of the gear axis or reference plane is calculated to obtain the numerical output of the tooth surface helical angle.

2. The method for measuring the inclined plane angle of an inclined gear according to claim 1, characterized in that: Methods for constructing mapping relationships include: Under the conditions of standard gears or calibration samples with known inclined plane angles, displacement parameters and mechanical parameters at different inclined plane angles are collected, and a basic dataset containing multiple inclined plane angle sample points is formed. The collected data is preprocessed to eliminate random noise introduced by workshop vibration and electromagnetic interference. The preprocessed displacement parameters and mechanical parameters are combined to construct a multidimensional feature vector, and the known inclined plane angle values ​​of different parts are labeled to form a "feature vector - inclined plane angle" correspondence. Based on the comparison relationship, a slope angle mapping function reflecting the combined effect of displacement parameters and mechanical parameters is established; The inclined plane angle mapping function was verified and optimized using a reference inclined plane gear with a known standard angle.

3. The method for measuring the inclined plane angle of a helical gear according to claim 1, characterized in that: The horizontal coordinate of the coordinate system represents the radial direction of the gear, denoted as the r-axis. The origin of the coordinate system is set at the intersection of the gear reference end face and the gear reference axis. The vertical coordinate represents the axial direction of the gear, denoted as the z-axis. When the upper value of the z-axis is zero, the z-axis coincides with the gear reference end face. The upper value of the z-axis is positive along the width direction of the gear.

4. The method for measuring the inclined plane angle of an inclined gear according to claim 1, characterized in that: For displacement parameters, the radial distance from the reference end face to the tooth surface contact point directly corresponds to the r coordinate value of the contact point in the coordinate system. The axial offset of the probe relative to the reference axis when it contacts the tooth surface corresponds to the z coordinate value of the contact point in the coordinate system. That is, each tooth surface contact point uniquely corresponds to a coordinate point (r, z) in the coordinate system.

5. The method for measuring the inclined plane angle of an inclined gear according to claim 1, characterized in that: For mechanical parameters, the direction of the normal force is along the normal direction of the tooth surface, which is used to decompose it into a component force in the r-axis direction and a component force in the z-axis direction. The direction of the mechanical parameter is associated with the position of the displacement parameter through the coordinate system.

6. The method for measuring the inclined plane angle of an inclined gear according to claim 1, characterized in that: Preset load conditions refer to the acquisition of displacement and mechanical parameters along the tooth length or tooth height direction within the measurement range of the tooth surface to be measured on the target inclined gear. Micro-displacement sampling refers to the acquisition of displacement sequences and corresponding mechanical response sequences along the selected measurement line of the target inclined gear in a continuous or segmented manner.

7. The method for measuring the inclined plane angle of an inclined gear according to claim 1, characterized in that: Methods for obtaining the normal vector include: The three-dimensional coordinates of the collected trajectory points are associated with the corresponding displacement parameters and mechanical parameters to form a local point cloud of the tooth surface; Based on the gear type of the helical gear, the fitting method is determined and the normal vector is obtained; For planar helical gears, the helical surface of a planar helical gear can be regarded as a plane unfolded along the tooth direction. Its geometric feature is that there is a fixed inclination angle only in the radial direction and the axial direction. For gears with twisted inclined planes, multiple sampling points are performed in the tooth direction using a probe to record the displacement changes at different tooth positions under the same radial-axial slope. Then, by combining the geometric relationship between the tooth direction and the radial and axial directions, the tilt angle of the inclined plane in the tooth direction can be deduced.

8. The method for measuring the inclined plane angle of an inclined gear according to claim 7, characterized in that: The inclination angle of a planar inclined gear is called the slope angle. When the probe gradually contacts the inclined plane from the reference end face of the gear, if the inclined plane is steeper, the probe will produce a larger axial displacement under the same radial displacement, thus increasing the value of the slope angle. Conversely, if the inclined plane is gentle, the displacement of the tactile probe along the axial direction is smaller, and the slope angle also decreases accordingly. For gears with twisted inclined planes, the inclination angle is the tooth inclination angle. By sampling multiple points along the tooth direction with a probe, the displacement changes at different tooth positions under the same radial-axial slope are recorded. Combined with the geometric relationship between the tooth direction and the radial and axial directions, the inclination angle of the inclined plane in the tooth direction can be deduced. When the tooth inclination angle is zero, it means that the inclined plane is only tilted in the radial-axial direction, with no tooth offset. The normal vector is the same as that of the planar inclined plane gear. When the tooth inclination angle increases, it means that the inclined plane has more significant twisting or helical movement in the tooth direction, and the normal vector gradually deviates from the radial-axial plane.

9. A device for measuring the angle of an inclined plane gear, characterized in that: The method for measuring the inclined plane angle of an inclined gear as described in any one of claims 1-8 was used.

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